Page 70 - Finite Element Analysis with ANSYS Workbench

Chapter

4

Plane Stress Analysis

Determination of deformation and stresses for two-
dimensional elasticity problems is rather difficult by using the
conventional approach. The finite element method alleviates such
difficulty especially for problems with complicated geometry. This
chapter begins with the governing differential equations of the
plane stress problem. Finite element equations and their element
matrices are derived for a simple triangular element. ANSYS with
its Workbench are employed to solve for solutions of examples in
both academic and application problems.

4.1 Basic Equations

4.1.1 Differential Equations

The equilibrium conditions at any point of a membrane
that lies in x-y plane, under in-plane forces with exclusion of body
forces, are governed by the two partial differential equations,